Question

The line 3x – 4y + 7 = 0 is rotated through an angle $\frac { \pi } { 4 }$ in the clockwise direction about the point (–1, 1). The equation of the line in its new position is-

• A. 7y + x – 6 = 0
• B. 7y – x – 6 = 0
• C. 7y + x + 6 = 0
• D. 7y – x + 6 = 0

Answer 1

Answer: (A)

7y + x – 6 = 0

Answer 2

1)

Sol. As (–1, 1) is a point on 3x – 4y + 7 = 0, the rotation is possible.

Slope of the given line = $\frac { 3 } { 4 }$.

Slope of the line in its new position = $\frac { \frac { 3 } { 4 } - 1 } { 1 + \frac { 3 } { 4 } }$= – $\frac { 1 } { 7 }$

The required equation is y – 1 = – $\frac { 1 } { 7 }$ (x + 1)

or 7y + x – 6 = 0.